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math: Use erff from CORE-MATH

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The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance to the generic erff.

The code was adapted to glibc style and to use the definition of
math_config.h.

Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (M1,
gcc 13.2.1), and powerpc (POWER10, gcc 13.2.1):

latency                       master       patched  improvement
x86_64                       85.7363       45.1372       47.35%
x86_64v2                     86.6337       38.5816       55.47%
x86_64v3                     71.3810       34.0843       52.25%
i686                         190.143       97.5014       48.72%
aarch64                      34.9091       14.9320       57.23%
power10                      38.6160        8.5188       77.94%
powerpc                      39.7446       8.45781       78.72%

reciprocal-throughput         master       patched  improvement
x86_64                       35.1739       14.7603       58.04%
x86_64v2                     34.5976       11.2283       67.55%
x86_64v3                     27.3260        9.8550       63.94%
i686                         91.0282       30.8840       66.07%
aarch64                      22.5831        6.9615       69.17%
power10                      18.0386        3.0918       82.86%
powerpc                      20.7277       3.63396       82.47%

Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella 2024-10-28 17:58:18 -03:00
parent c4c64ba5d1
commit 994fec2397
28 changed files with 251 additions and 235 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
SHARED-FILES
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@ -272,3 +272,7 @@ sysdeps/ieee754/flt-32/s_cbrtf.c
(file src/binary32/cbrt/cbrtf.c in CORE-MATH)
- The code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow.
sysdeps/ieee754/flt-32/s_erff.c
(file src/binary32/erf/erff.c in CORE-MATH)
- The code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow.

1
sysdeps/aarch64/libm-test-ulps
View File

@ -991,7 +991,6 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_advsimd":

4
sysdeps/alpha/fpu/libm-test-ulps
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@ -909,22 +909,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

4
sysdeps/arc/fpu/libm-test-ulps
View File

@ -733,19 +733,15 @@ float: 6
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 2
Function: "erf_upward":
double: 2
float: 2
Function: "erfc":
double: 5

1
sysdeps/arc/nofpu/libm-test-ulps
View File

@ -177,7 +177,6 @@ float: 2
Function: "erf":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/arm/libm-test-ulps
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@ -726,19 +726,15 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/csky/fpu/libm-test-ulps
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@ -719,19 +719,15 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/csky/nofpu/libm-test-ulps
View File

@ -717,19 +717,15 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/hppa/fpu/libm-test-ulps
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@ -742,20 +742,16 @@ float: 3
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/i386/fpu/libm-test-ulps
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@ -1078,25 +1078,21 @@ ldouble: 3
Function: "erf":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
float128: 2
ldouble: 1
Function: "erf_towardzero":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
float128: 2
ldouble: 1

4
sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
View File

@ -1081,25 +1081,21 @@ ldouble: 3
Function: "erf":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
float128: 2
ldouble: 1
Function: "erf_towardzero":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
float128: 2
ldouble: 1

392
sysdeps/ieee754/flt-32/s_erff.c
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@ -1,154 +1,256 @@
/* s_erff.c -- float version of s_erf.c.
*/
/* Correctly-rounded error function for binary32 value.
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
Copyright (c) 2022-2024 Alexei Sibidanov.
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
#endif
This file is part of the CORE-MATH project
project (file src/binary32/erf/erff.c revision bc385c2).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#include <errno.h>
#include <float.h>
#include <math.h>
#include <math-narrow-eval.h>
#include <math_private.h>
#include <math-underflow.h>
#include <stdint.h>
#include <libm-alias-float.h>
#include <fix-int-fp-convert-zero.h>
#include "math_config.h"
static const float
tiny = 1e-30,
one = 1.0000000000e+00, /* 0x3F800000 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
pp1 = -3.2504209876e-01, /* 0xbea66beb */
pp2 = -2.8481749818e-02, /* 0xbce9528f */
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
qq4 = 1.3249473704e-04, /* 0x390aee49 */
qq5 = -3.9602282413e-06, /* 0xb684e21a */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
qa4 = 1.2617121637e-01, /* 0x3e013307 */
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
ra2 = -1.0558626175e+01, /* 0xc128f022 */
ra3 = -6.2375331879e+01, /* 0xc2798057 */
ra4 = -1.6239666748e+02, /* 0xc322658c */
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
ra7 = -9.8143291473e+00, /* 0xc11d077e */
sa1 = 1.9651271820e+01, /* 0x419d35ce */
sa2 = 1.3765776062e+02, /* 0x4309a863 */
sa3 = 4.3456588745e+02, /* 0x43d9486f */
sa4 = 6.4538726807e+02, /* 0x442158c9 */
sa5 = 4.2900814819e+02, /* 0x43d6810b */
sa6 = 1.0863500214e+02, /* 0x42d9451f */
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
rb2 = -1.7757955551e+01, /* 0xc18e104b */
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
rb5 = -1.0250950928e+03, /* 0xc480230b */
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
sb3 = 1.5367296143e+03, /* 0x44c01759 */
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
sb5 = 2.5530502930e+03, /* 0x451f90ce */
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
float __erff(float x)
float
__erff (float x)
{
int32_t hx,ix,i;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erf(nan)=nan */
i = ((uint32_t)hx>>31)<<1;
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x31800000) { /* |x|<2**-28 */
if (ix < 0x04000000)
{
/* Avoid spurious underflow. */
float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
math_check_force_underflow (ret);
return ret;
}
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(z,ix&0xfffff000);
r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
/* for 7 <= i < 63, C[i-7] is a degree-7 polynomial approximation of
erf(i/16+1/32+x) for -1/32 <= x <= 1/32 */
static const double C[56][8] = {
{ 0x1.f86faa9428f9cp-2, 0x1.cfc41e36c7dfap-1, -0x1.b2c7dc53508b9p-2,
-0x1.5a9de93fa556ep-3, 0x1.731793dbb01b5p-3, 0x1.133e06426cf18p-6,
-0x1.a12a6289cafd8p-5, 0x1.717d6f1d6f557p-9 },
{ 0x1.1855a5fd3dd50p-1, 0x1.b3aafcc27502fp-1, -0x1.cee5ac8e92bb2p-2,
-0x1.fa02983ca2d79p-4, 0x1.77cd746cb1922p-3, -0x1.fa6f277886487p-10,
-0x1.8de75458db416p-5, 0x1.00899c98551c9p-7 },
{ 0x1.32a54cb8db67ap-1, 0x1.96164fafd8de5p-1, -0x1.e23a7ea0c9ad3p-2,
-0x1.3f5ee15671cf4p-4, 0x1.70e468a3d72d9p-3, -0x1.3da68037cfc99p-6,
-0x1.69ed9ba1f9839p-5, 0x1.8cab9244a4ff4p-7 },
{ 0x1.4b13713ad3513p-1, 0x1.7791b886e7405p-1, -0x1.ecef423109bf5p-2,
-0x1.15c3c5cec6847p-5, 0x1.5f688fc931ba6p-3, -0x1.1da63ed190037p-5,
-0x1.38427ca63cca4p-5, 0x1.fa00e52525e17p-7 },
{ 0x1.61955607dd15dp-1, 0x1.58a445da7c74ep-1, -0x1.ef6c246a0f66cp-2,
0x1.e83e0d9d61330p-8, 0x1.44cc65535bc9fp-3, -0x1.87d3c4860435dp-5,
-0x1.f90b10501169bp-6, 0x1.22295856d427ap-6 },
{ 0x1.762870f720c6fp-1, 0x1.39ccc1b136d5cp-1, -0x1.ea4feea4e4744p-2,
0x1.715e5952ebfbap-5, 0x1.22cdbd83c75c4p-3, -0x1.da50aa1d925b6p-5,
-0x1.754dc0a29b4ddp-6, 0x1.350b6bef9392cp-6 },
{ 0x1.88d1cd474a2e0p-1, 0x1.1b7e98fe26219p-1, -0x1.de65a22ce1419p-2,
0x1.40686a3f16400p-4, 0x1.f6b0cbb216b2bp-4, -0x1.09c7c903edd57p-4,
-0x1.da7529fde641p-7, 0x1.362a7a0588eabp-6 },
{ 0x1.999d4192a5717p-1, 0x1.fc3ee5d1524b3p-2, -0x1.cc990045b55c8p-2,
0x1.b37338e68b37dp-4, 0x1.a0d120c872ea7p-4, -0x1.19bb2b07ecff6p-4,
-0x1.a110f5f593aafp-8, 0x1.272c15a57720ep-6 },
{ 0x1.a89c850b7d54dp-1, 0x1.c40b0729ed54ap-2, -0x1.b5eaaef0a2346p-2,
0x1.0847c7dacbae1p-3, 0x1.47de0ba6d18fbp-4, -0x1.1d9de77a4b648p-4,
0x1.30ffbe56f0726p-10, 0x1.0a9cb99feea01p-6 },
{ 0x1.b5e62fce16096p-1, 0x1.8eed36b886d95p-2, -0x1.9b64a06e50705p-2,
0x1.2bb6e2c744df5p-3, 0x1.dee3261ca61bcp-5, -0x1.16996004f7da5p-4,
0x1.fdff37bae983ep-8, 0x1.c750083e65f9ap-7 },
{ 0x1.c194b1d49a184p-1, 0x1.5d4fd33729015p-2, -0x1.7e0f4f045addbp-2,
0x1.444bc66c31a1bp-3, 0x1.356dbf16ec8f1p-5, -0x1.0643de0906cd8p-4,
0x1.b281af7bd3a2cp-7, 0x1.6b97eaa2c6abdp-7 },
{ 0x1.cbc54b476248ep-1, 0x1.2f7cc3fe6f423p-2, -0x1.5ee8429e36de8p-2,
0x1.52a8395f96177p-3, 0x1.313761ba257dcp-6, -0x1.dcf844d5fed8fp-5,
0x1.1e1420f475fa9p-6, 0x1.091c7dc1e18b2p-7 },
{ 0x1.d4970f9ce00d9p-1, 0x1.059f59af7a905p-2, -0x1.3eda354de36c3p-2,
0x1.57b85ad439779p-3, 0x1.8e913b9778136p-10, -0x1.a2893bd3435f4p-5,
0x1.4d3a90e37164ap-6, 0x1.4ce7f6e19a902p-8 },
{ 0x1.dc29fb60715b0p-1, 0x1.bf8e1b1ca2277p-3, -0x1.1eb7095e5d6d2p-2,
0x1.549ea6f7a64f4p-3, -0x1.b10f12f3877a3p-7, -0x1.61420c8f7156ap-5,
0x1.674f1f92a8812p-6, 0x1.25543ffd74d52p-9 },
{ 0x1.e29e22a89d767p-1, 0x1.7bd5c7df3fe99p-3, -0x1.fe674494077bfp-3,
0x1.4a9feacf86578p-3, -0x1.a008269076644p-6, -0x1.1cf0e8fb4f1cbp-5,
0x1.6e0d2ef105fb3p-6, -0x1.367205fbd7876p-12 },
{ 0x1.e812fc64db36ap-1, 0x1.3fda6bc016991p-3, -0x1.c1cb278627920p-3,
0x1.3b10512314f1ep-3, -0x1.1e6457bb1b9a9p-5, -0x1.b1f6474e2388cp-6,
0x1.640a5345f7ec7p-6, -0x1.3dae5a997fdbp-9 },
{ 0x1.eca6ccd709544p-1, 0x1.0b3f52ce8c380p-3, -0x1.8885019f63c6dp-3,
0x1.274275fc91a05p-3, -0x1.57f73699a8372p-5, -0x1.3076a305fc7cep-6,
0x1.4c6ae04843a41p-6, -0x1.0be5fcf5ecc91p-8 },
{ 0x1.f0762fde45ee7p-1, 0x1.bb1c972f23e4ap-4, -0x1.5341e3c01b58dp-3,
0x1.107929f6f0b60p-3, -0x1.7e1b34f976c02p-5, -0x1.73b62589c234ap-7,
0x1.2a97ee1876486p-6, -0x1.595f40a3150fep-8 },
{ 0x1.f39bc242e43e6p-1, 0x1.6c7e64e7281c5p-4, -0x1.2274b86835fd3p-3,
0x1.efb890e5c770dp-4, -0x1.92c7db16847e0p-5, -0x1.45477db5e2dd4p-8,
0x1.01fc6165fc866p-6, -0x1.8845509030c2cp-8 },
{ 0x1.f62fe80272419p-1, 0x1.297db960e4f5dp-4, -0x1.ecb83b087c04fp-4,
0x1.bce18363ca3d1p-4, -0x1.985aaf776482cp-5, 0x1.cd953efdae886p-12,
0x1.ab9a0b89b54ffp-7, -0x1.9b5e576ccc31cp-8 },
{ 0x1.f848acb544e95p-1, 0x1.e1d4cf1e24501p-5, -0x1.9e12e1fde5552p-4,
0x1.8a27806df3d1bp-4, -0x1.91674e5eb3319p-5, 0x1.3bc75595b2db8p-8,
0x1.51bc537ac61afp-7, -0x1.96b23b19ea04dp-8 },
{ 0x1.f9f9ba8d3c733p-1, 0x1.83298d7172108p-5, -0x1.58d101f905a75p-4,
0x1.58f1456f8639bp-4, -0x1.808d1850b8231p-5, 0x1.0c1bd99c348a7p-7,
0x1.f61e9d7bc48cap-8, -0x1.7f07c13441774p-8 },
{ 0x1.fb54641aebbc9p-1, 0x1.34ac36ad8dafap-5, -0x1.1c8ec267f9405p-4,
0x1.2a52c5d841848p-4, -0x1.68541c02b3b6bp-5, 0x1.5afe400196379p-7,
0x1.565b2d6eda3d6p-8, -0x1.596aaff29e739p-8 },
{ 0x1.fc67bcf2d7b8fp-1, 0x1.e85c449e377efp-6, -0x1.d177f166c07c6p-5,
0x1.fe23b7584b504p-5, -0x1.4b12109613313p-5, 0x1.8d9905c0acf7dp-7,
0x1.9265032a669dap-9, -0x1.2ac4a6dbcbf3ep-8 },
{ 0x1.fd40bd6d7a785p-1, 0x1.7f5188610ddc7p-6, -0x1.7954423f7c998p-5,
0x1.af5baae33887fp-5, -0x1.2ad77c7cbc474p-5, 0x1.a7b8c47ec2a51p-7,
0x1.46646ee094bccp-10, -0x1.ef19d8db8673p-9 },
{ 0x1.fdea6e062d0c9p-1, 0x1.2a875b5ffab58p-6, -0x1.2f3178cd6dcd5p-5,
0x1.68d1c45b94182p-5, -0x1.09648ed3aeaefp-5, 0x1.ad8b150d38164p-7,
-0x1.e9a6023d9429fp-13, -0x1.8722d19ee2e8ep-9 },
{ 0x1.fe6e1742f7cf5p-1, 0x1.cd5ec93c1243ap-7, -0x1.e2ff3aaacb386p-6,
0x1.2aa4e5823cc89p-5, -0x1.d049842dbe399p-6, 0x1.a34edb21ab302p-7,
-0x1.676e5996c7f9bp-10, -0x1.23b01a35140bfp-9 },
{ 0x1.fed37386190fbp-1, 0x1.61beae53b72c2p-7, -0x1.7d6193f22c3c1p-6,
0x1.e947279e3bb7dp-6, -0x1.906031b97ca97p-6, 0x1.8d14d62561755p-7,
-0x1.1f245e7178882p-9, -0x1.9257d4eb47685p-10 },
{ 0x1.ff20e0a7ba8c2p-1, 0x1.0d1d69569b839p-7, -0x1.2a8ca0dc02752p-6,
0x1.8cc071b709751p-6, -0x1.54a149f1b070cp-6, 0x1.6e9137b13412cp-7,
-0x1.6577ed3d8e83bp-9, -0x1.e9c1a5178a289p-11 },
{ 0x1.ff5b8fb26f5f6p-1, 0x1.9646f35a7663cp-8, -0x1.cf68ed9311b0bp-7,
0x1.3e8735b5a694fp-6, -0x1.1e1612d026fdfp-6, 0x1.4afd8e6ca636dp-7,
-0x1.8c375170ccb22p-9, -0x1.c799443c4fd3bp-12 },
{ 0x1.ff87b1913e853p-1, 0x1.30499b5039596p-8, -0x1.64964201ec8bap-7,
0x1.fa73d7eafba98p-7, -0x1.daa3022141fbbp-7, 0x1.2509444c063b7p-7,
-0x1.99482a2f8a0a1p-9, -0x1.403d1f76c9454p-15 },
{ 0x1.ffa89fe5b3625p-1, 0x1.c4412bf4b8f35p-9, -0x1.100f347126cf0p-7,
0x1.8ebda07671d40p-7, -0x1.850c6a31c98c1p-7, 0x1.fdac860c67d21p-8,
-0x1.927d03d2ba12cp-9, 0x1.0ff620b4190fep-12 },
{ 0x1.ffc10194fcb64p-1, 0x1.4d78bba8ca621p-9, -0x1.9ba107a443e02p-8,
0x1.36f273fbc04ccp-7, -0x1.3b38716ac7e6fp-7, 0x1.b3fe0181914acp-8,
-0x1.7d3fe7de98c5cp-9, 0x1.ea31f8e5317f7p-12 },
{ 0x1.ffd2eae369a07p-1, 0x1.e7f232d9e266cp-10, -0x1.34c7442dd48d9p-8,
0x1.e066bed070a0bp-8, -0x1.f914f3c42fc0dp-8, 0x1.6f4664ed2260fp-8,
-0x1.5e59910761d24p-9, 0x1.39cbb6e84c126p-11 },
{ 0x1.ffdff92db56e5p-1, 0x1.6235fbd7a4373p-10, -0x1.cb5e029b9e56ap-9,
0x1.6fa4c7ef274dap-8, -0x1.903a089a835f3p-8, 0x1.30f12e0ca1901p-8,
-0x1.39d21b6957f99p-9, 0x1.5d3f8495a703cp-11 },
{ 0x1.ffe96a78a04a9p-1, 0x1.fe41cd9bb4f2cp-11, -0x1.52d7b28966c0cp-9,
0x1.16c192d86a1a7p-8, -0x1.39bfce951100cp-8, 0x1.f376a7869f9e3p-9,
-0x1.12e6cef999c4fp-9, 0x1.66acd4d667b5p-11 },
{ 0x1.fff0312b010b5p-1, 0x1.6caa0d3583018p-11, -0x1.efb729f4cf75bp-10,
0x1.a2da7cebe12acp-9, -0x1.e6c27a24bc759p-9, 0x1.93b1f4d8ea65p-9,
-0x1.d82050aa94a08p-10, 0x1.5cd7dc75d6cbap-11 },
{ 0x1.fff50456dab8cp-1, 0x1.0295ef6591865p-11, -0x1.679880e95a4dap-10,
0x1.37d38e3a5c8ebp-9, -0x1.75b3708aebb8fp-9, 0x1.4231c4b4b0296p-9,
-0x1.8e26476489318p-10, 0x1.45c3b570dd924p-11 },
{ 0x1.fff86cfd3e657p-1, 0x1.6be02102b353dp-12, -0x1.02b157780d6aep-10,
0x1.cc1d886861133p-10, -0x1.1bff6f12ec9abp-9, 0x1.fc0f77bd9c736p-10,
-0x1.4a3320bd0959dp-10, 0x1.267f8b4f95d2p-11 },
{ 0x1.fffad0b901755p-1, 0x1.fc0d55470cf5ep-13, -0x1.7121aff5e820ep-11,
0x1.506d6992f7de5p-10, -0x1.ab595d3ecd0d6p-10, 0x1.8bdd79daaf754p-10,
-0x1.0d9b090f997c1p-10, 0x1.031ab9fd1c7dap-11 },
{ 0x1.fffc7a37857d2p-1, 0x1.5feada379d8a5p-13, -0x1.05304df58f3aap-11,
0x1.e79c081b8600fp-11, -0x1.3e5dbe33232e0p-10, 0x1.30eb208200729p-10,
-0x1.b1d493b147945p-11, 0x1.bd587bbc071bep-12 },
{ 0x1.fffd9fdeabccep-1, 0x1.e3bcf436a1a49p-14, -0x1.6e953111ef0a1p-12,
0x1.5e3edf6768654p-11, -0x1.d5be67c0547a4p-11, 0x1.d07d9ffa1d435p-11,
-0x1.58328f5f358cap-11, 0x1.76d42d95c42c4p-12 },
{ 0x1.fffe68f4fa777p-1, 0x1.49e17724f4cddp-14, -0x1.fe48c44e229c1p-13,
0x1.f2bd95d76f188p-12, -0x1.57388cb12d011p-11, 0x1.5decc25c5c079p-11,
-0x1.0d7499d1b0d2dp-11, 0x1.359332c94ecdcp-12 },
{ 0x1.fffef1960d85dp-1, 0x1.be6abbb10a4cdp-15, -0x1.6040381a8c313p-13,
0x1.5fff1dde9ee9dp-12, -0x1.f0c933efa9971p-12, 0x1.04cbf4a5cd760p-11,
-0x1.a07f150af6dadp-12, 0x1.f68dd183426bap-13 },
{ 0x1.ffff4db27f146p-1, 0x1.2bb5cc22e5cd8p-15, -0x1.e25894899f526p-14,
0x1.ec8a8e5a72757p-13, -0x1.64256ae0a3cf9p-12, 0x1.80a836c18c46cp-12,
-0x1.3dea401af6775p-12, 0x1.915ddff3fe0d1p-13 },
{ 0x1.ffff8b500e77cp-1, 0x1.8f4ccca7fc769p-16, -0x1.478cffe305946p-14,
0x1.559f04adde504p-13, -0x1.f9e1577d6961dp-13, 0x1.18bda53c14716p-12,
-0x1.df8634c35541cp-13, 0x1.3bb5c6b616337p-13 },
{ 0x1.ffffb43555b5fp-1, 0x1.07ebd2a2d26c8p-16, -0x1.b93e442a37f2bp-15,
0x1.d5cf15159ce28p-14, -0x1.63f5e1469c006p-13, 0x1.95a03acebac18p-13,
-0x1.656e5e2a1f8e2p-13, 0x1.e98c437189bdep-14 },
{ 0x1.ffffcf23ff5fcp-1, 0x1.5a2adfa0b492cp-17, -0x1.26c88270759f0p-15,
0x1.40473572b99a8p-14, -0x1.f057cbde578a5p-14, 0x1.22178d1c3c948p-13,
-0x1.0765b61a0d859p-13, 0x1.765b3ea03ddbep-14 },
{ 0x1.ffffe0bd3e852p-1, 0x1.c282cd3957a72p-18, -0x1.86ad6dfa44faap-16,
0x1.b0f313f03a029p-15, -0x1.56e44abecd255p-14, 0x1.9ad1ecfe34a89p-14,
-0x1.7fe4033478618p-14, 0x1.1a8184e049fbfp-14 },
{ 0x1.ffffec2641a9ep-1, 0x1.22df29821407ep-18, -0x1.00c902a6cfd98p-16,
0x1.22234eb88671fp-15, -0x1.d57a181c9e6e1p-15, 0x1.200c283b54a90p-14,
-0x1.14b4c3295a7d0p-14, 0x1.a4f966f713bdep-15 },
{ 0x1.fffff37d63a36p-1, 0x1.74adc8f405eecp-19, -0x1.4ed4228e44858p-17,
0x1.81918baea92bap-16, -0x1.3e81b17a0009cp-15, 0x1.9004a36116436p-15,
-0x1.8aa1ba400e076p-15, 0x1.35cd4e2340a9ep-15 },
{ 0x1.fffff82cdcf1bp-1, 0x1.d9c73698fa87dp-20, -0x1.b11017ec67115p-18,
0x1.fc0dfadf653f8p-17, -0x1.ac4e03cd2dfc2p-16, 0x1.131806b5abbc5p-15,
-0x1.1672ef66fcaafp-15, 0x1.c2882c7debed7p-16 },
{ 0x1.fffffb248c39dp-1, 0x1.2acee2f5ec66ap-20, -0x1.15cc570408a36p-18,
0x1.4be757bbb75a3p-17, -0x1.1d6aa5f8d2940p-16, 0x1.76c5937d5105ep-16,
-0x1.84dffc3ca9302p-16, 0x1.43c8315f2c30ap-16 },
{ 0x1.fffffd01f36afp-1, 0x1.75fa8dbc840bap-21, -0x1.6186da0133f5ap-19,
0x1.ae023231e1af5p-18, -0x1.790812f7ca394p-17, 0x1.f9c25656d0ef2p-17,
-0x1.0cc66682e304cp-16, 0x1.cc170a75d6f9cp-17 },
{ 0x1.fffffe2ba0ea5p-1, 0x1.d06ad6ecde88ep-22, -0x1.be46aa8edc9a1p-20,
0x1.143860c7840b8p-18, -0x1.edaba78fb1260p-18, 0x1.52138a96ecee2p-17,
-0x1.6fca538c4e2eep-17, 0x1.434040640bcefp-17 },
{ 0x1.fffffee3cc32cp-1, 0x1.1e1e857adb8ddp-22, -0x1.1769ce5f2a6e8p-20,
0x1.5fe5d479b0543p-19, -0x1.405d865c94c2ap-18, 0x1.bfc94feb96afcp-18,
-0x1.f245d5f3e8358p-18, 0x1.c142456acf443p-18 },
};
float ax = fabsf (x);
uint32_t ux = asuint (ax);
double s = x;
double z = ax;
/* 0x407ad444 corresponds to x = 0x1.f5a888p+1 = 3.91921..., which is the
largest float such that erf(x) does not round to 1 (to nearest). */
if (__glibc_unlikely (ux > 0x407ad444u))
{
float os = copysignf (1.0f, x);
if (ux > (0xffu << 23))
return x + x; /* nan */
if (ux == (0xffu << 23))
return os; /* +-inf */
return os - 0x1p-25f * os;
}
double v = floor (16.0 * z);
uint32_t i = 16.0f * ax;
/* 0x3ee00000 corresponds to x = 0.4375, for smaller x we have i < 7. */
if (__glibc_unlikely (ux < 0x3ee00000u))
{
static const double c[] =
{
0x1.20dd750429b6dp+0, -0x1.812746b0375fbp-2,
0x1.ce2f219fd6f45p-4, -0x1.b82ce2cbf0838p-6,
0x1.565bb655adb85p-8, -0x1.c025bfc879c94p-11,
0x1.f81718f61309cp-14, -0x1.cc67bd88f5867p-17
};
double z2 = s * s, z4 = z2 * z2, z8 = z4 * z4;
double c0 = c[0] + z2 * c[1];
double c2 = c[2] + z2 * c[3];
double c4 = c[4] + z2 * c[5];
double c6 = c[6] + z2 * c[7];
c0 += z4 * c2;
c4 += z4 * c6;
c0 += z8 * c4;
return s * c0;
}
z = (z - 0.03125) - 0.0625 * v;
const double *c = C[i - 7];
double z2 = z * z, z4 = z2 * z2;
double c0 = c[0] + z * c[1];
double c2 = c[2] + z * c[3];
double c4 = c[4] + z * c[5];
double c6 = c[6] + z * c[7];
c0 += z2 * c2;
c4 += z2 * c6;
c0 += z4 * c4;
return copysign (c0, s);
}
libm_alias_float (__erf, erf)

4
sysdeps/loongarch/lp64/libm-test-ulps
View File

@ -910,22 +910,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

4
sysdeps/m68k/m680x0/fpu/libm-test-ulps
View File

@ -839,21 +839,17 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 1
Function: "erfc":

1
sysdeps/microblaze/libm-test-ulps
View File

@ -172,7 +172,6 @@ float: 2
Function: "erf":
double: 1
float: 1
Function: "erfc":
double: 3

4
sysdeps/mips/mips32/libm-test-ulps
View File

@ -723,19 +723,15 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/mips/mips64/libm-test-ulps
View File

@ -909,22 +909,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

1
sysdeps/nios2/libm-test-ulps
View File

@ -177,7 +177,6 @@ float: 2
Function: "erf":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/or1k/fpu/libm-test-ulps
View File

@ -723,19 +723,15 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/or1k/nofpu/libm-test-ulps
View File

@ -723,19 +723,15 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_downward":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erf_upward":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/powerpc/fpu/libm-test-ulps
View File

@ -1105,25 +1105,21 @@ double: 1
Function: "erf":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
float128: 2
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
float128: 1
ldouble: 2
Function: "erf_upward":
double: 1
float: 1
float128: 2
ldouble: 3

4
sysdeps/powerpc/nofpu/libm-test-ulps
View File

@ -919,22 +919,18 @@ double: 1
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 2
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

4
sysdeps/riscv/nofpu/libm-test-ulps
View File

@ -906,22 +906,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

4
sysdeps/riscv/rvd/libm-test-ulps
View File

@ -909,22 +909,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

4
sysdeps/s390/fpu/libm-test-ulps
View File

@ -910,22 +910,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

2
sysdeps/sh/libm-test-ulps
View File

@ -355,11 +355,9 @@ float: 3
Function: "erf":
double: 1
float: 1
Function: "erf_towardzero":
double: 1
float: 1
Function: "erfc":
double: 5

4
sysdeps/sparc/fpu/libm-test-ulps
View File

@ -909,22 +909,18 @@ ldouble: 5
Function: "erf":
double: 1
float: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
ldouble: 2
Function: "erf_towardzero":
double: 1
float: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
ldouble: 2
Function: "erfc":

4
sysdeps/x86_64/fpu/libm-test-ulps
View File

@ -1290,25 +1290,21 @@ ldouble: 3
Function: "erf":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_downward":
double: 1
float: 1
float128: 2
ldouble: 1
Function: "erf_towardzero":
double: 1
float: 1
float128: 1
ldouble: 1
Function: "erf_upward":
double: 1
float: 1
float128: 2
ldouble: 1